# Proof in Group Theory

Let C* be the multiplicative group of nonzero complex numbers and R** be the multiplicative group of positive real numbers. Prove that C* is isomorphic to R** X R/Z where R is the additive group of real numbers.

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#### Solution Preview

We wish to show that where is the additive group of real numbers, is the multiplicative group of positive real numbers, and is the multiplicative group of nonzero complex numbers.

Consider ...

#### Solution Summary

We prove that the multiplicative group of nonzero complex numbers is isomorphic to the direct product of the multiplicative group of positive real numbers and the additive group of real number modulo the integers.

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